1MA0 Higher June 2015 Paper 2 Q2
2 The equation
\[x^3 - x^2 = 30\]has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| 3.5 | 4 | B2 for a trial \(3.4 \leqslant x \leqslant 3.5\) evaluated correctly (B1 for a trial evaluated correctly for \(3 \leqslant x \leqslant 4\)) B1 for a different trial evaluated correctly for \(3.45 \leqslant x \lt 3.5\) B1 (dep on at least one previous B1) for 3.5 [Note: Trials should be evaluated to at least accuracy shown in table, truncated or rounded] [NB No working scores 0 marks] |
Working
| \(x\) | \(x^3 - x^2\) |
|---|---|
| 3 | 18 |
| 3.1 | 20.(181) |
| 3.2 | 22.(528) |
| 3.3 | 25.(047) |
| 3.4 | 27.(744) |
| 3.5 | 30.(625) |
| 3.6 | 33.(696) |
| 3.7 | 36.(963) |
| 3.8 | 40.(432) |
| 3.9 | 44.(109) |
| 4 | 48 |
| 3.45 | 29.1(61125) |
| 3.46 | 29.4(50136) |
| 3.47 | 29.7(41023) |
| 3.48 | 30.0(33792) |
| 3.49 | 30.3(28449) |